Quebec Mathematical Sciences Colloquium

December 1, 2006 from 16:00 to 18:00 (Montreal/Miami time) On location

The Sato-Tate conjecture

Colloquium presented by Richard Taylor (Harvard University)

A fixed elliptic curve over the rational numbers is known to have approximately p points modulo p for any prime number p. In about 1960 Sato and Tate gave a conjectural distribution for the error term. Laurent Clozel, Michael Harris, Nick Shepherd-Barron and I recently proved this conjecture in the case that the elliptic curve has somewhere multiplicative reduction. In this talk I will describe the Sato-Tate conjecture and the ideas Tate and Serre had for proving it. I will also sketch how we were able to prove sufficient higher dimensional modularity results to complete the proof.


UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., Salle / Room SH-3420